From the Smalltalk world, I'm pretty much interested in every single tweet. Besides, people in this group don't tweet that much.
As for musicians and bands, we usually follow each other in order to stay aware of gigs, recordings, etc. But following is also an act of befriending, so there are bands and individuals who tweet way too much but to whom I still want to show interest, so I can't unfollow them.
Friends and acquaintances from my town, however, you've got to follow them... and some of them are really annoying. I don't want to unfollow them because, as OP said, «few of them might get offended and then your relations might ruin or something like that». If you live in a small enough town, you'll know what I mean :)
But as a gesture of politeness, you might want to follow someone who has followed you and is close to you, but at the same time you would not want to listen to all his tweets, in that case, silence might work, and not unfollowing.
Well, yeah. Who are these people that you want to silence but don't want to unfollow? What would unfollowing do, which you don't want, which silencing would not do?